Question

Bradley solved the following equation:

4(5x – 6) = 2(8x + 10)


Step Work Justification
1 20x – 24 = 16x + 20
2 4x – 24 = 20
3 4x = 44
4 x = 11


Which of the following has all correct justifications Bradley used to solve this equation?
1. Associative property of addition. 2. Subtraction property of equality. 3. Addition property of equality. 4. Multiplicative inverse.
1. Associative property of addition. 2. Subtraction property of equality. 3. Addition property of equality. 4. Division property of equality.
1. Distributive property. 2. Subtraction property of equality. 3. Addition property of equality. 4. Multiplicative property of equality.
1. Distributive property. 2. Subtraction property of equality. 3. Addition property of equality. 4. Division property of equality.

Answer 1

The correct answer is D.

I will go through each step detailing the property used.

Given the base equation, simplify and solve for x.

4(5x - 6) = 2(8x + 10)

Using the distributive property, distribute each term outside the parentheses to each term within the parentheses.

20x - 24 = 16x + 20

Next, using the subtraction property of equality, subtract 16x from both sides.

4x - 24 = 20

Now, using the addition property of equality, add 24 to both sides.

4x = 44

And finally, using the division property of equality, divide both sides by 4.

x = 11